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Finite Volume Analysis of Relativistic Field Theories Using Lattice Regularization

使用格正则化的相对论场论的有限体积分析

基本信息

批准号：
1913010
负责人：
Rajamani Narayanan
金额：
$ 24.03万
依托单位：
Florida International University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-07-15 至 2024-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1913010&HistoricalAwards=false
关键词：
Finite Volume Analysis Relativistic Field

项目摘要

Quantum Chromo Dynamics (QCD) is a theory that describes one of the fundamental interactions in nature, namely, strong interactions. The fundamental degrees of freedom are quarks (particles) and gluons (force mediators). Gauge fields (gluons) coupled to massless fermions (quarks) have no free parameters and they have no intrinsic scale. Depending on the nature of the gauge group and the fermionic content, these theories fall into two categories upon quantization: One that maintains scale invariance and contains only massless excitations and one that breaks scale invariance and produces a rich spectrum of massive excitations. Whether the quantum theory is scale invariant or not, it is always strongly interacting and a non-perturbative formalism is necessary to study why some theories are scale invariant and the others are not. It is also necessary to study the flow from one theory to another and try to understand how a scale emerges. The PI will extract properties of theories in both classes (scale invariant and scale breaking) and study the flow of a scale invariant theory to a theory that breaks scale invariance. This will enable us to understand the emergence of the fundamental scale in strong interactions.Lattice formalism of gauge fields coupled to massless fermions is a well tested approach to the extraction of the fundamental non-perturbative properties of these theories. Theories that break scale invariance have been studied in great detail using this method. The PI will use the lattice formalism and study potentially scale invariant theories in a finite periodic box. The size of the box sets an external scale and the PI will be able to extract the scale invariant properties of a theory by studying the asymptotic behavior as a function of the external scale. By fixing the gauge group and varying the number of fermion flavors by one unit around a critical number of fermion flavors the PI will start with one theory (larger number of fermion flavors) and add a mass term for one of the fermion flavors. By varying the mass parameter from zero to infinity, the PI will be able to flow between two theories where both of them are scale invariant at the classical level but one (fewer number of fermion flavors) breaks the scale invariance at the quantum level.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

量子色动力学(QCD)是一种描述自然界中最基本的相互作用之一，即强相互作用的理论。基本自由度是夸克(粒子)和胶子(力介体)。与无质量费米子(夸克)耦合的规范场(胶子)没有自由参数，也没有本征标度。根据规范群的性质和费米子含量的不同，这些理论在量子化后分为两类：一类保持标度不变性，只包含无质量激发；另一类打破标度不变性，产生丰富的大量激发谱。无论量子理论是不是尺度不变的，它总是强相互作用的，需要一个非微扰的形式论来研究为什么一些理论是尺度不变的，而另一些则不是。还有必要研究从一种理论到另一种理论的流动，并试图理解规模是如何出现的。PI将提取这两类理论(标度不变和标度破坏)的属性，并研究标度不变理论到打破标度不变的理论的流动。这将使我们能够理解在强相互作用中基本标度的出现。规范场与无质量费米子耦合的格子形式是提取这些理论基本非微扰性质的一种经过检验的方法。用这种方法对打破标度不变性的理论进行了详细的研究。PI将使用格子形式，并研究有限周期盒中的潜在标度不变理论。盒子的大小设置了一个外部标度，PI将能够通过研究作为外部标度的函数的渐近行为来提取理论的标度不变属性。通过固定规范群并将费米子口味的数量围绕关键数量的费米子口味改变一个单位，PI将从一个理论(更大数量的费米子口味)开始，并为其中一种费米子口味添加一个质量项。通过将质量参数从零改变到无穷大，PI将能够在两个理论之间流动，其中两个理论在经典水平上都是尺度不变的，但其中一个(较少的费米子味道)打破了量子水平的尺度不变性。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。